A. E. Shabad

Photon dispersion in a strong magnetic field

Abstract In an external magnetic field analytical properties are studied of the photon polarization tensor calculated as the electron-positron loop in the Furry picture. The polarization tensor is reexpressed as a sum over singular contributions coming from e + e − -pair photocreation in semidiscrete Landau states. The solutions of the photon dispersion equation (i.e., the one for the poles of the photon propagator) are described. The shape of the photon dispersion curve obtained is responsible for the effect of photon deflection by a strong magnetic field. No physically reliable solutions, apart from spurions, are found for the longitudinal photon mode. An infinite number of solutions with complex space-momentum are found, with no apparnet ghosts among them. An attempt is made to interprete the former in terms of possible bound and quasibound states of electron and positron pairs.

Polarization of relativistic electron and positron gas in a strong magnetic field. Propagation of electromagnetic waves

Abstract Structural properties of the polarization operator, Greens function, and electromagnetic eigenmodes for relativistic electron-positron gas placed in a magnetic field at a nonzero temperature are established based on the most general consideration of unitarity and the properties under gauge and Lorentz transformations, charge conjugation, inversion of space, and the 4-velocity of the medium. Polarizations of the eigenmodes are described in the general form. Connection between the charge asymmetry and the appearance of elliptic polarization is formally established. For each eigenmode one of the principal axes of the polarization ellipse lies in the plane containing the external magnetic field and the direction of the wave propagation, while the other is orthogonal to this plane. The polarization operator is calculated within the one-loop approximation of the Furry picture within the technique of the temperature Greens functions [1] with the subsequent analytical continuation of the frequency. The results obtained are valid also for a uniformly moving medium.

Absorption and dispersion of electromagnetic eigenwaves of electron-positron plasma in a strong magnetic field

Abstract The investigation of the electromagnetic properties of an electron-positron gas placed in a strong magnetic field at nonzero temperature (initiated in (H. Perez Rojas and A. E. Shabad, Ann. Phys. (N. Y.)121 (1979), 432)) is continued in this paper. The analytic properties of the polarization operator in the one-loop approximation are established and its antihermitian part is calculated. It shows an infinite behavior near the thresholds of absorption, due to the processes of excitation and electron-positron pair creation. Using the optical theorem, expressions are given for the photon absorption probabilities in terms of the antihermitian part of the polarization operator. The imaginary part of the dielectric constant and the absorption probabilities are calculated for the case of wave propagation along the external magnetic field. The allowed regions for absorption in momentum space for the zero temperature limit, are discussed. Forbidden domains appear due to the Pauli exclusion principle. The singular (inverse square root) behavior of the polarization operator near the thresholds is used to solve the dispersion equations. As a result, it is found that the improved expressions for the probabilities of absorption must remain finite at the thresholds. Expressions are also given for the photon masses near the first excitation thresholds.

SUPERCONDUCTIVITY IN DENSE ELECTROWEAK SYSTEM

The spectrum of fermions in the presence of the W-boson-condensed electro-weak liquid is obtained and nonvanishing spatial component of the fermionic polarization operator is calculated for zero 4-momentum. The manifestation of the Meissner effect is studied. The London penetration depth λL is calculated in the limit of small W-condensate amplitude. The possibility of a special phenomenon of partial magnetic screening due to the mixing angle dependence on the leptonic density is discussed in connection with the magnetic mass problem.

Bose-Einstein condensation in many-particle gauge theories and external charge

SummaryThe realization of the charged Bose-Einstein condensation in gauge theories with finite particle density is investigated. Examples are found for a situation in which two charged Bose-Einstein condensates coexist in equilibrium in systems described by Abelian gauge theories. Also Abelian and non-Abelian systems are constructed for which a charged Bose-Einstein condensate is balanced by the charge of a fermionic subsystem. A limiting transition to infinitely heavy fermions with infinite chemical potential is pointed out, which turns the fermionic subsystem into an external charge in an Abelian theory. On the contrary, the non-Abelian gauge theory with external charge cannot be obtained by the same dynamical limiting process since it requires a special quantization scheme. It is realized for the Yang-Mills-Higgs model with a constant external charge. Eigenfrequencies of the system are found, which include an additional quantum degree of freedom induced by the external charge. The contribution of the eigenfrequencies to the thermodynamical potential is found.RiassuntoSi studia la realizzazione della condensazione di Bose-Einstein carica nelle teorie di gauge con densità finita di particelle. Si trovano esempi di una situazione in cui coesistono due condensati di Bose-Einstein carichi in equilibrio in sistemi descritti dalle teorie di gauge abeliane. Si costruiscono inoltre sistemi abeliani e non abeliani per i quali un condensato di Bose-Einstein carico è bilanciato dalla carica di un sottosistema fermionico. Si evidenzia una transizione limitativa a fermioni infinitamente pesanti con potenziale chimico infinito, che trasforma il sottosistema fermionico in una carica esterna in una teoria abeliana. Al contrario, la teoria di gauge non abeliana con carica esterna non può essere ottenuta con lo stesso processo dinamico limitativo, poiché richiede uno schema di quantizzazione speciale. Questo si realizza per il modello di Jang-Mills-Higgs con carica esterna costante. Si trovano le autofrequenze del sistema che includono un grado quantistico aggiuntivo di libertà indotto dalla carica esterna. Si trova il contributo delle autofrequenze al potenziale termodinamico.РезюмеИсследуется реализация заряженной конденсации Бозе-Эйнштейна в калибровочных тэориях с конечной плотностью частиц. Рассматриваются примеры такой ситуации, когда два заряженных конденсата Бозе-Эйнштейна сосуществуют в равновесии в системах, описываемых абелевыми калибровочными теориями. Также конструируутся абелевы и неабелевы системы, для которых заряженный конденсат Бозе-Эйнштейна уравновешивается зарядом фермионной подсистемы. Отмечается предельный переход к бесконечно тяжелым фермионам с бесконечным химическим потенциадом, которыи превращает фермионную подсистему во внешний заряд в абелевой теории. Неабелева калибровочная теория с внешним зарядом не может быть получена с помощью такого динамическото предельного перехода, так как требует специальной схемы квантования. Предлагается реализация для модели Янга-Миллса-Хиггса с постоянным внешним зарядом. Определяются собственные частоты системы, которые включают дополнительныю квантовую степень свободы, связанную с внешним зарядом. Вычисляется вклад собственных частот в термодинамический потенциал.

FERMIONIC SUPERCONDUCTIVITY IN THE DENSE WEINBERG-SALAM MODEL

The superconducting behavior of the W-condensate phase of the Weinberg-Salam liquid is investigated. The removal of the W-orientation degeneracy by a small external electromagnetic field imposed on the W-condensate is found. Against the background of the condensed W-mesons the left-lepton spectrum undergoes a restructuring with the appearance of an energy gap between all the particle-antiparticle states, and the joining of particles and antiparticles in the new spectrum. Some of these peculiarities are indicated as a signal of the electrical superconductivity of such a medium. The definitive conclusions about the fermion superconductivity are achieved by studying the contribution to the London’s equation of the one-fermion loop polarization operator against the W-condensate background at zero momentum. The London’s penetration depth λL is found in the limit of small W-condensate amplitude.

Partial magnetic screening by the electroweak vacuum

The authors investigate the linear response of the Higgs vacuum of the electroweak model to a magnetic field applied from a neighbouring domain labelled by a different isotopic orientation of the Higgs field expectation value. The authors obtain that the applied magnetic field BA is screened down to the value BA cos2 2 theta W within a London depth of the order of Mz-1, while a quasimagnetic weak-neutral field Bz is induced, reaching at the same characteristic depth the asymptotic value 1/2BA sin 4 theta W. The working mechanism of the superconducting currents responsible for this effect is discussed.

Photon magnetic mass and Meissner effect in the Bose-Einstein condensate of W-mesons

Abstract It is shown that in the W-condensate phase reached in the electroweak plasma when the fermion density JL is increased above some critical value ( J L ⋍ M W 3 6π the residual UEM(1) symmetry of the Weinberg-Salam model is spontaneously broken. Starting from the effective action of the W-condensate phase, calculated within the approximation known to guarantee the Bose-Einstein condensation of W±-mesons, we diagonalize the mass matrix of bosons and calculate the photon magnetic mass that proves to be different from zero as a consequence of the spontaneous violation of the UEM(1)-symmetry. By solving the linearized set of coupled equations for the photon, W- and Z-boson fields, we find that a small magnetic field applied from outside penetrates into the W-condensate medium down to the Londons depth equal to the photon magnetic mass inversed and also induces W- and Z-fields in the same layer of the medium. This Meissner effect is performed by a polarization charge of weak nature induced on the surface and by an electric and weak supercurrents concentrated at the depth of inversed weak mesons masses (MW ≈ M L ).

Kondyensatsiya Bozye-Ei{cyrillic, short}nshtyei{cyrillic, short}na v mnogochastichnykh kalibrovochnykh tyeoriyakh i vnyeshnii{cyrillic, short} zaryad

SummaryThe realization of the charged Bose-Einstein condensation in gauge theories with finite particle density is investigated. Examples are found for a situation in which two charged Bose-Einstein condensates coexist in equilibrium in systems described by Abelian gauge theories. Also Abelian and non-Abelian systems are constructed for which a charged Bose-Einstein condensate is balanced by the charge of a fermionic subsystem. A limiting transition to infinitely heavy fermions with infinite chemical potential is pointed out, which turns the fermionic subsystem into an external charge in an Abelian theory. On the contrary, the non-Abelian gauge theory with external charge cannot be obtained by the same dynamical limiting process since it requires a special quantization scheme. It is realized for the Yang-Mills-Higgs model with a constant external charge. Eigenfrequencies of the system are found, which include an additional quantum degree of freedom induced by the external charge. The contribution of the eigenfrequencies to the thermodynamical potential is found.RiassuntoSi studia la realizzazione della condensazione di Bose-Einstein carica nelle teorie di gauge con densità finita di particelle. Si trovano esempi di una situazione in cui coesistono due condensati di Bose-Einstein carichi in equilibrio in sistemi descritti dalle teorie di gauge abeliane. Si costruiscono inoltre sistemi abeliani e non abeliani per i quali un condensato di Bose-Einstein carico è bilanciato dalla carica di un sottosistema fermionico. Si evidenzia una transizione limitativa a fermioni infinitamente pesanti con potenziale chimico infinito, che trasforma il sottosistema fermionico in una carica esterna in una teoria abeliana. Al contrario, la teoria di gauge non abeliana con carica esterna non può essere ottenuta con lo stesso processo dinamico limitativo, poiché richiede uno schema di quantizzazione speciale. Questo si realizza per il modello di Jang-Mills-Higgs con carica esterna costante. Si trovano le autofrequenze del sistema che includono un grado quantistico aggiuntivo di libertà indotto dalla carica esterna. Si trova il contributo delle autofrequenze al potenziale termodinamico.РезюмеИсследуется реализация заряженной конденсации Бозе-Эйнштейна в калибровочных тэориях с конечной плотностью частиц. Рассматриваются примеры такой ситуации, когда два заряженных конденсата Бозе-Эйнштейна сосуществуют в равновесии в системах, описываемых абелевыми калибровочными теориями. Также конструируутся абелевы и неабелевы системы, для которых заряженный конденсат Бозе-Эйнштейна уравновешивается зарядом фермионной подсистемы. Отмечается предельный переход к бесконечно тяжелым фермионам с бесконечным химическим потенциадом, которыи превращает фермионную подсистему во внешний заряд в абелевой теории. Неабелева калибровочная теория с внешним зарядом не может быть получена с помощью такого динамическото предельного перехода, так как требует специальной схемы квантования. Предлагается реализация для модели Янга-Миллса-Хиггса с постоянным внешним зарядом. Определяются собственные частоты системы, которые включают дополнительныю квантовую степень свободы, связанную с внешним зарядом. Вычисляется вклад собственных частот в термодинамический потенциал.

Bose-Einstein condensation in many-particle gauge theories and external charge@@@Конденсация Бозе-Эйнштейна в многочастичных калибровочных теориях и внешний заряд

SummaryThe realization of the charged Bose-Einstein condensation in gauge theories with finite particle density is investigated. Examples are found for a situation in which two charged Bose-Einstein condensates coexist in equilibrium in systems described by Abelian gauge theories. Also Abelian and non-Abelian systems are constructed for which a charged Bose-Einstein condensate is balanced by the charge of a fermionic subsystem. A limiting transition to infinitely heavy fermions with infinite chemical potential is pointed out, which turns the fermionic subsystem into an external charge in an Abelian theory. On the contrary, the non-Abelian gauge theory with external charge cannot be obtained by the same dynamical limiting process since it requires a special quantization scheme. It is realized for the Yang-Mills-Higgs model with a constant external charge. Eigenfrequencies of the system are found, which include an additional quantum degree of freedom induced by the external charge. The contribution of the eigenfrequencies to the thermodynamical potential is found.RiassuntoSi studia la realizzazione della condensazione di Bose-Einstein carica nelle teorie di gauge con densità finita di particelle. Si trovano esempi di una situazione in cui coesistono due condensati di Bose-Einstein carichi in equilibrio in sistemi descritti dalle teorie di gauge abeliane. Si costruiscono inoltre sistemi abeliani e non abeliani per i quali un condensato di Bose-Einstein carico è bilanciato dalla carica di un sottosistema fermionico. Si evidenzia una transizione limitativa a fermioni infinitamente pesanti con potenziale chimico infinito, che trasforma il sottosistema fermionico in una carica esterna in una teoria abeliana. Al contrario, la teoria di gauge non abeliana con carica esterna non può essere ottenuta con lo stesso processo dinamico limitativo, poiché richiede uno schema di quantizzazione speciale. Questo si realizza per il modello di Jang-Mills-Higgs con carica esterna costante. Si trovano le autofrequenze del sistema che includono un grado quantistico aggiuntivo di libertà indotto dalla carica esterna. Si trova il contributo delle autofrequenze al potenziale termodinamico.РезюмеИсследуется реализация заряженной конденсации Бозе-Эйнштейна в калибровочных тэориях с конечной плотностью частиц. Рассматриваются примеры такой ситуации, когда два заряженных конденсата Бозе-Эйнштейна сосуществуют в равновесии в системах, описываемых абелевыми калибровочными теориями. Также конструируутся абелевы и неабелевы системы, для которых заряженный конденсат Бозе-Эйнштейна уравновешивается зарядом фермионной подсистемы. Отмечается предельный переход к бесконечно тяжелым фермионам с бесконечным химическим потенциадом, которыи превращает фермионную подсистему во внешний заряд в абелевой теории. Неабелева калибровочная теория с внешним зарядом не может быть получена с помощью такого динамическото предельного перехода, так как требует специальной схемы квантования. Предлагается реализация для модели Янга-Миллса-Хиггса с постоянным внешним зарядом. Определяются собственные частоты системы, которые включают дополнительныю квантовую степень свободы, связанную с внешним зарядом. Вычисляется вклад собственных частот в термодинамический потенциал.